Question: Let $g(x)=x^{^{\scriptsize\dfrac{1}{4}}}$. $g'(x)=$
Answer: The derivative of $g$ can be found using the power rule : $\dfrac{d}{dx}(x^n)=n\cdot x^{n-1}$ (Remember that this applies even when $n$ is a fraction.) $\begin{aligned} &\phantom{=}g'(x) \\\\ &=\dfrac{d}{dx}\left(x^{^{\frac{1}{4}}}\right) \\\\ &=\dfrac{1}{4}x^{^{\frac{1}{4}-1}} \gray{\text{The power rule}} \\\\ &=\dfrac14x^{^{-\frac{3}{4}}} \end{aligned}$ In conclusion, we found that $g'(x)=\dfrac14x^{^{-\frac{3}{4}}}$. This can also be written as $\dfrac{1}{4\sqrt[4]{x^3}}$ (all equivalent forms are accepted).